The Contribution of Transport and Human Capital Infrastructure to Local Private Production: A Partial Adjustment Approach

This paper uses a partial adjustment approach to measure the contribution of public infrastructure to local private production. In the first step of the empirical analysis we apply a principal component analysis in order to construct 2 new infrastructure indicators from an array of 7 measures of transport and human capital infrastructure. In the second step the output of different sectors is regressed on private factor inputs and on these 2 infrastructure indicators. Our main finding is that expected long-run equilibrium output in an area of local government will be higher, the better it is endowed with both transport and human capital infrastructure. Moreover, transport and human capital infrastructure appear to be complementary, i.e. raising only transport infrastructure will not yield an increase in private production at the local level. ZUSAMMENFASSUNG - (Der Beitrag von Verkehrs- und Humankapitalinfrastruktur zur lokalen privaten Produktion: Ein "partial adjustment" Ansatz) Diese Studie verwendet einen "partial adjustment" Ansatz, um den Beitrag von öffentlicher Infrastruktur zur privaten Produktion auf der lokalen Ebene zu bestimmen. Im ersten Schritt der empirischen Analyse wird eine Hauptkomponentenanalyse durchgeführt, um 2 neue Infrastrukturindikatoren aus 7 Variablen für Verkehrs- und Humankapitalinfrastruktur zu bestimmen. Im zweiten Schritt wird der Output von verschiedenen Sektoren auf die privaten Faktorinputs sowie die 2 gefundenen Infrastrukturindikatoren regressiert. Das wichtigste empirische Ergebnis der Analyse ist, daß der erwartete langfristige Gleichgewichtsoutput in einem Kreis höher ist, je besser die Ausstattung sowohl mit Verkehrs- wie auch mit Humankapitalinfrastruktur ist. Weiterhin finden wir, daß Verkehrs- und Humankapitalinfrastruktur zueinander komplementär sind, d.h. falls nur die Ausstattung mit Verkehrsinfrastruktur verbessert würde, daraus keine Erhöhung der privaten lokalen Produktion resultiert.

On the Cox ring of blowing up the diagonal

We compute the Cox rings of the blow-ups $\mathrm{Bl}_\Delta(X'\times X')$ and $\mathrm{Bl}_\Delta(\mathbb P_1^n)$ where $X'$ is a product of projective spaces and $\Delta$ is the (generalised) diagonal.Comment: 8 page

The influence of random element displacement on DOA estimates obtained with (Khatri-Rao-)root-MUSIC

Although a wide range of direction of arrival (DOA) estimation algorithms has been described for a diverse range of array configurations, no specific stochastic analysis framework has been established to assess the probability density function of the error on DOA estimates due to random errors in the array geometry. Therefore, we propose a stochastic collocation method that relies on a generalized polynomial chaos expansion to connect the statistical distribution of random position errors to the resulting distribution of the DOA estimates. We apply this technique to the conventional root-MUSIC and the Khatri-Rao-root-MUSIC methods. According to Monte-Carlo simulations, this novel approach yields a speedup by a factor of more than 100 in terms of CPU-time for a one-dimensional case and by a factor of 56 for a two-dimensional case

Orthogonality of Hermite polynomials in superspace and Mehler type formulae

In this paper, Hermite polynomials related to quantum systems with orthogonal O(m)-symmetry, finite reflection group symmetry G < O(m), symplectic symmetry Sp(2n) and superspace symmetry O(m) x Sp(2n) are considered. After an overview of the results for O(m) and G, the orthogonality of the Hermite polynomials related to Sp(2n) is obtained with respect to the Berezin integral. As a consequence, an extension of the Mehler formula for the classical Hermite polynomials to Grassmann algebras is proven. Next, Hermite polynomials in a full superspace with O(m) x Sp(2n) symmetry are considered. It is shown that they are not orthogonal with respect to the canonically defined inner product. However, a new inner product is introduced which behaves correctly with respect to the structure of harmonic polynomials on superspace. This inner product allows to restore the orthogonality of the Hermite polynomials and also restores the hermiticity of a class of Schroedinger operators in superspace. Subsequently, a Mehler formula for the full superspace is obtained, thus yielding an eigenfunction decomposition of the super Fourier transform. Finally, an extensive comparison is made of the results in the different types of symmetry.Comment: Proc. London Math. Soc. (2011) (42pp

Linear equations with unknowns from a multiplicative group in a function field

Let k be an algebraically closed field of characteristic 0, let K/k be a transcendental extension of arbitrary transcendence degree and let G be a multiplicative subgroup of (K^*)^n such that (k^*)^n is contained in G, and G/(k^*)^n has finite rank r. We consider linear equations a1x1+...+anxn=1 (*) with fixed non-zero coefficients a1,...,an from K, and with unknowns (x1,...,xn) from the group G. Such a solution is called degenerate if there is a subset of a1x1,...,anxn whose sum equals 0. Two solutions (x1,...,xn), (y1,...,yn) are said to belong to the same (k^*)^n-coset if there are c1,...,cn in k^* such that y1=c1*x1,...,yn=cn*xn. We show that the non-degenerate solutions of (*) lie in at most 1+C(3,2)^r+C(4,2)^r+...+C(n+1,2)^r (k^*)^n-cosets, where C(a,b) denotes the binomial coefficient a choose b.Comment: 15 pages, LaTeX fil

Class invariants for certain non-holomorphic modular functions

Inspired by prior work of Bruinier and Ono and Mertens and Rolen, we study class polynomials for non-holomorphic modular functions arising from modular forms of negative weight. In particular, we give general conditions for the irreducibility of class polynomials. This allows us to easily generate infintely many new class invariants

Computing endomorphism rings of abelian varieties of dimension two

Generalizing a method of Sutherland and the author for elliptic curves, we design a subexponential algorithm for computing the endomorphism rings of ordinary abelian varieties of dimension two over finite fields. Although its correctness and complexity analysis rest on several assumptions, we report on practical computations showing that it performs very well and can easily handle previously intractable cases.Comment: 14 pages, 2 figure

Fundamental Limits of Optical Force and Torque

Optical force and torque provide unprecedented control on the spatial motion of small particles. A valid scientific question, that has many practical implications, concerns the existence of fundamental upper bounds for the achievable force and torque exerted by a plane wave illumination with a given intensity. Here, while studying isotropic particles, we show that different light-matter interaction channels contribute to the exerted force and torque; and analytically derive upper bounds for each of the contributions. Specific examples for particles that achieve those upper bounds are provided. We study how and to which extent different contributions can add up to result in the maximum optical force and torque. Our insights are important for applications ranging from molecular sorting, particle manipulation, nanorobotics up to ambitious projects such as laser-propelled spaceships.Comment: 5 pages, 5 figures, 2 tables, Supplemental Material (27 pages, 6 figures